Efficient coupling of light between one optical fiber and another, or between an electro-optic device and an optical fiber requires that the optical fiber have a mirror-like end surface perpendicular to the axis of the fiber. This condition must be met regardless of whether the coupling involves simple end-to-end coupling of optical fibers or the mounting of a microlens on the fiber end surface. Typically, a fiber is cleaved by scoring a surface at the desired point and then applying a tensile stress to the fiber, causing a crack to propagate across the fiber from the point of scoring. This method of cleaving often produces an irregular surface, particularly for fibers having a diameter less than about 20 micrometers. This problem becomes particularly important for single mode fibers where the fiber has been thinned by removal of a portion of the fiber cladding prior to cleaving. It would be desirable to have a method for cleaving an optical fiber, particularly a fiber having a small diameter, which is both simple, economical, and produces a mirror-like end surface on a fiber having a uniform or tapered diameter.